@nathansmarked , as I see it from your original post , all the interactions and the current response ( I thank you for the quick and detailed answer ), there are multiple issues here :
(a) as far the original question of , if you can file MFJ with your wife -- YES. Even though she does not have an ITIN , you can still file jointly, requesting that your spouse be treated as a resident -- this will indeed expose her world income ( if any ) to US taxes. Till her status is changed from B-2 to a work visa or Green Card, she is eligible for ITIN for purposes of filing a return ( in this case jointly with a US citizen)
(b) Till your spouse gets a work permission or status change ( allowing work ) she cannot get an SSN .
(c) I am very confused about your reference to Economic Impact Payment/Credit -- as a Non-Resident Alien, she is not eligible for such credit/payment. Question here is what happens when an NRA is treated as Resident for Tax purposes -- does that submission once accepted , make that person eligible for economic Impact Payment , at least for the 2021 ( the tax year when he/she is being treated as resident for tax purposes . I have to research this a bit more , but I suspect the answer would be yes).
(d) Another concern I have is that if she entered USA on B-2 ( a six month visa ) in Nov. 2020, even with an extension of another six months, by Dec 2021 , she would have been out of status---- thus creating an issue with the processing the Green Card application. Just wondering why did you not get a K visa or similar so she could be regularized. What visa is she under now while being married ? Is she in "out of status" ? Perhaps you should consult an immigration lawyer. Since she has become a student, why did she not get her visa changed to F-1?
Here are two references that may help :
ITIN / IRS ----https://www.irs.gov/instructions/iw7#en_US_202112_publink54092gd0e107
SSA -- https://www.ssa.gov/pubs/EN-05-10096.pdf
Does this answer your query or is there more I can do for you ?
pk
